Some Basic Hypergeometric Orthogonal Polynomials That Generalize Jacobi Polynomials PDF Download
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Author | : Richard Askey |
Publisher | : American Mathematical Soc. |
Total Pages | : 63 |
Release | : 1985 |
Genre | : Jacobi polynomials |
ISBN | : 0821823213 |
Download Some Basic Hypergeometric Orthogonal Polynomials that Generalize Jacobi Polynomials Book in PDF, ePub and Kindle
A very general set of orthogonal polynomials in one variable that extends the classical polynomials is a set we called the q-Racah polynomials. In an earlier paper we gave the orthogonality relation for these polynomials when the orthogonality is purely discrete. We now give the weight function in the general case and a number of other properties of these very interesting orthogonal polynomials.
Author | : Richard Askey |
Publisher | : |
Total Pages | : 55 |
Release | : 1986 |
Genre | : |
ISBN | : |
Download Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials Book in PDF, ePub and Kindle
Author | : Richard Askey |
Publisher | : |
Total Pages | : 55 |
Release | : 1985 |
Genre | : |
ISBN | : |
Download Some Basic Hypergeometric Orthogonal Polynomial that Generalize Jacobi Polynomials Book in PDF, ePub and Kindle
Author | : Roelof Koekoek |
Publisher | : Springer Science & Business Media |
Total Pages | : 584 |
Release | : 2010-03-18 |
Genre | : Mathematics |
ISBN | : 364205014X |
Download Hypergeometric Orthogonal Polynomials and Their q-Analogues Book in PDF, ePub and Kindle
The present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all families in the (q-)Askey scheme classical orthogonal polynomials, and to call the Jacobi, Laguerre and Hermite polynomials very classical orthogonal polynomials. These very classical orthogonal polynomials are good friends of mine since - most the beginning of my mathematical career. When I was a fresh PhD student at the Mathematical Centre (now CWI) in Amsterdam, Dick Askey spent a sabbatical there during the academic year 1969–1970. He lectured to us in a very stimulating wayabouthypergeometricfunctionsandclassicalorthogonalpolynomials. Evenb- ter, he gave us problems to solve which might be worth a PhD. He also pointed out to us that there was more than just Jacobi, Laguerre and Hermite polynomials, for instance Hahn polynomials, and that it was one of the merits of the Higher Transc- dental Functions (Bateman project) that it included some newer stuff like the Hahn polynomials (see [198, §10. 23]).
Author | : Richard A. Askey |
Publisher | : |
Total Pages | : 55 |
Release | : 1985 |
Genre | : |
ISBN | : |
Download Some Basic Hypergeometric. Orthogonal Polynomials That, Generalize Jacobipolynomilas Book in PDF, ePub and Kindle
Author | : Sister Mary Céline Fasenmyer |
Publisher | : |
Total Pages | : 16 |
Release | : 1947 |
Genre | : Functions, Hypergeometric |
ISBN | : |
Download Some Generalized Hypergeometric Polynomials Book in PDF, ePub and Kindle
Author | : Jan Felipe Van Diejen |
Publisher | : American Mathematical Soc. |
Total Pages | : 290 |
Release | : 1999 |
Genre | : Fonctions spéciales - Congrès |
ISBN | : 0821820265 |
Download Algebraic Methods and $q$-Special Functions Book in PDF, ePub and Kindle
There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.
Author | : Howard S. Cohl |
Publisher | : Cambridge University Press |
Total Pages | : 352 |
Release | : 2020-10-15 |
Genre | : Mathematics |
ISBN | : 1108905420 |
Download Lectures on Orthogonal Polynomials and Special Functions Book in PDF, ePub and Kindle
Written by experts in their respective fields, this collection of pedagogic surveys provides detailed insight and background into five separate areas at the forefront of modern research in orthogonal polynomials and special functions at a level suited to graduate students. A broad range of topics are introduced including exceptional orthogonal polynomials, q-series, applications of spectral theory to special functions, elliptic hypergeometric functions, and combinatorics of orthogonal polynomials. Exercises, examples and some open problems are provided. The volume is derived from lectures presented at the OPSF-S6 Summer School at the University of Maryland, and has been carefully edited to provide a coherent and consistent entry point for graduate students and newcomers.
Author | : Ranjan Roy |
Publisher | : Cambridge University Press |
Total Pages | : 479 |
Release | : 2021-03-18 |
Genre | : Mathematics |
ISBN | : 1108709370 |
Download Series and Products in the Development of Mathematics Book in PDF, ePub and Kindle
Second of two volumes tracing the development of series and products. Second edition adds extensive material from original works.
Author | : Ranjan Roy |
Publisher | : Cambridge University Press |
Total Pages | : |
Release | : 2021-03-18 |
Genre | : Mathematics |
ISBN | : 1108573185 |
Download Series and Products in the Development of Mathematics: Volume 1 Book in PDF, ePub and Kindle
This is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.